math Legendre problem

Initial conditions p(0)=1 and p(1)=x , we also have that p(n+1)=((2*n+1)*x*p(n)-n*p(n-1))/(n+1).

As we all know, matlab cannt start from p(0), therefor i do this :

p(1)=1, p(2)=x and p(n)=((2*n-1)*x*p(n-1)-(n-1)*p(n-2))/n

but i DON'T take the same results and i don't know the reason !! As you see i am working with Legendre Polynomials !!

Thanks !!

Answer 1

[Geoff]

That's almost right, but wherever you had p(n) etc, you shouldn't adjust n. You should only have subtracted 1 from the instances of n that are on their own. So change all your p(??) bits back to their original values and it should work.

[George]

i think i did it but still doesn't work. i propably missunderstood what you 've told me to do.. can you explain it to me again please ?

[Geoff]

Hmmm I might have done this backwards. It depends whether you define 'n' with its original meaning, or if you use a new 'n' that means something else!

Let's go with keeping the original meaning. In that case, your original formula is correct except for anywhere it indexes into 'p'. So you would just add 1 to 'n' inside any of the p-vector references, and don't touch it anywhere else.

You are trying to preserve the meaning of 'n', but change the indexing of 'p'.

[George]

can you please write down the formula ??? Thanks !!

[George]

p(k+2) = ((2*k+1)*x*p(k+1) - (k)*p(k))/(k+1) ;

i think i've got it right now !!!! THANKS !!!!